The included anlgle mention in two line segement and the line meet at a common point is said to be included angle. In triangle included anlges is divided into three category, they are acute angle triangle, obtuse angle triangle, and right angle triangles In this article we will discuss about included angle of a triangle with suitable example problems.

**Included anlge:**

**on the basis of included angle , the triangle are classified into three types they are shown in the below.**

- Right angle triangle
- Acute angle triangle
- Obtuse angle triangle

**Right angle triangle:**

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Here the angle 90^{0} is included to Qp and QR. If one of the angle is 90^{0} then it is called right angle triangle the total angles is
180^{0}

**Acute angle triangle:**

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Any one of the included angle of a traingle ABC, BAC and ACB is less than 90^{0}. Then it is said to be acute angle triangle the total angle is 180^{o}.

**Obtuse angle triangle:**

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Here the angle is included of a triangle BA and BC 110^{o} .if any one of the angle is greater than 90^{o} then it is said to be obtuse
angle triangle the total angle is 180^{o}.

**Identifying the angle of a triangle**

**Problem (i): If the sum of included angle of right angle triangle is 180 ^{o} the angles are 40^{o} and 50^{o}.Find the other
angle**

**Solution:**

If the sum of included angle of right angle triangle is 180^{o} the angles are 40^{o} and 50^{o} .Find the other angle

**Step 1: ^{ }** Here a+b+c = 180

**Step 2: **50^{o} +40^{o}+c = 180^{o}

90^{o }+c = ^{ }180^{o}

**step 3: **Subtracting both sides by 90^{o}

90^{o }+C-90^{o} = ^{ }180^{o} -90^{o}

c = 90^{o}

**step 4:** The angle is 90^{o}

**Problem (ii): If the sum of included angle of acute triangle is 180 ^{o} the angles are 60^{o} and 20^{o}**

**Solution:**

If the sum of included angle of acute triangle is 180^{o} the angles are 60^{o} and 20^{o}. Find the other angle

**Step 1: ^{ }** Here a+b+c = 180

**Step 2: **60^{o} +20^{o}+c = 180^{o}

80^{o }+c = ^{ }180^{o}

**step 3: **Subtracting both sides by 80^{o}

80^{o }+C-80^{o} = ^{ }180^{o} -80^{o}

C = 100^{o}

**step 4:** The other angle is 100^{o}.